84 W. P. Trowbridge—Hficiency of Steam Boilers. 
qds=cWdt from which FD Aoi’ 
Introducing now the law of Dulong and Petit, by sub- 
- stituting for q its equivalent C’t'?**, the expression becomes 
cWdt de t=? "#8 ai, 
=O yrass me eW e 
Integrating between the limits 4, and ¢, we obtain 
8 a ih by PR lce 
ae ~"333.(7 
from which the value of ¢, may be obtained, 
t= OWi ys eee 
\cW —'233 0S. t, (298 
In this expression S represents the whole heating surface of 
the boiler, or the surface of the tube, a known quantity; 7, may 
be ascertained by observation with a common thermometer. 
But no accurate mode of ascertaining 4, by observation has 
yet been found, and hence the necessity of this mode of deter- 
mination. 
In the second member of the equation the undetermined 
quantities are W and C’, the first representing the weight of 
gas which passes through the furnace in an hour, and the 
second the constant C’ of the formula of Dulong and Petit. 
e taken on the assumption, generally acquiesced in, that 
in ordinary boilers the quantity of air which passes through the 
furnace is just double the quantity necessary for perfect com- 
bustion, and we assume for C’ the value given by Mr. Hopkins 
for carbonic acid gas, the value of ¢, is completely determined; 
and to find the initial temperature of the gases, it will be only 
necessary to observe, with the aid of a common thermometer, 
the temperature of the gases at their exit from the tube or 
boiler. Having found 4, the quantity of heat transferred by 
contact of the gases, in the flues, to the water, will be 
represented by 
W(4—2)- 
c 
The value of Q then becomes 
Q=C. af. (a’—1). G+F. 0.4299 +¢W (4-4). 
in which all the terms become known, except the first term of 
' the second member. 
The value of the expression G@XxC.a?(a'—1) being thus — 
determined, the separate influence of the radiant heat of the 
furnace becomes known, and the value of ¢, the difference of the 
temperature between the fuel and the water, may, by the aid of 
Hopkins’ value of C, be ascertained. 
